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Definitions
===========
Leading dimensions
------------------
Many algorithms can be applied exactly the same to a variable even though it may have different dimension dependencies.
For instance, a density conversion can be the same algorithm for either `density {}`, `density {time}`,
`density {latitude,longitude}`, `density {time,vertical}`, etc.
The algorithm is just applied element-wise for each element in the dimensions that `density` depends on.
Such leading dimensions that can be handled element-wise are captured by a ':' in the variable reference in the
definitions below.
Any dimensions that are significant for the conversion (for instance, the `vertical` dimension when integrating a
vertical profile to a total column) will still be mentioned explicitly and will map to an index in the symbol used for
the quantity (e.g. :math:`\nu(:,i)`). If an algorithm has variables with a ':' in the dimension specification then the
algorithm will contain a description of which combination of dimensions are supported for ':'.
Constants
---------
=================== ============================ ================================ ===============================
symbol name unit value
=================== ============================ ================================ ===============================
:math:`a` WGS84 semi-major axis :math:`m` :math:`6378137.0`
:math:`b` WGS84 semi-minor axis :math:`m` :math:`6356752.314245`
:math:`c` speed of light :math:`\frac{m}{s}` :math:`2.99792458\cdot10^{8}`
:math:`\frac{1}{f}` WGS84 inverse flatting :math:`298.257223563`
:math:`g_{0}` mean earth gravity :math:`\frac{m}{s^2}` :math:`9.80665`
:math:`g_{e}` earth gravity at equator :math:`\frac{m}{s^2}` :math:`9.7803253359`
:math:`g_{p}` earth gravity at poles :math:`\frac{m}{s^2}` :math:`9.8321849378`
:math:`GM` WGS84 earth's gravitational :math:`\frac{m^3}{s^2}` :math:`3986004.418\cdot10^{8}`
constant
:math:`k` Boltzmann constant :math:`\frac{kg m^2}{K s^2}` :math:`1.38064852\cdot10^{-23}`
:math:`N_A` Avogadro constant :math:`\frac{1}{mol}` :math:`6.022140857\cdot10^{23}`
:math:`p_{0}` standard pressure :math:`Pa` :math:`101325`
:math:`R` universal gas constant :math:`\frac{kg m^2}{K mol s^2}` :math:`8.3144598`
:math:`T_{0}` standard temperature :math:`K` :math:`273.15`
:math:`\omega` WGS84 earth angular velocity :math:`rad/s` :math:`7292115.0\cdot10^{-11}`
=================== ============================ ================================ ===============================
Molar mass
----------
The following table provides for each species the molar mass :math:`M_{x}` in :math:`\frac{g}{mol}`.
See the documentation on the HARP data format for a description of all species.
======= =================================================
name molar mass
======= =================================================
dry air 28.9644
BrO 95.9034
BrO2 111.9028
CCl2F2 120.9135
CCl3F 137.3681
CCl4 153.822
CF4 88.00431
CHClF2 86.4684
CH3Cl 50.48752
CH3CN 41.05192
CH3OH 32.04186
CH4 16.0425
CO 28.0101
COF2 66.0069
COS 60.0751
CO2 44.0095
C2H2 26.0373
C2H2O2 58.036163
C2H6 30.0690
C2H3NO5 121.04892
C3H8 44.09562
C5H8 68.11702
ClNO3 97.4579
ClO 51.4524
HCHO 30.026
HCOOH 46.0254
HCN 27.0253
HCl 36.4609
HF 20.006343
HNO2 47.013494
HNO3 63.0129
HNO4 79.0122
HOCl 52.4603
HO2 33.00674
H2O 18.0153
H2O_161 1.00782503207 + 15.99491461956 + 1.00782503207
H2O_162 1.00782503207 + 15.99491461956 + 2.0141017778
H2O_171 1.00782503207 + 16.99913170 + 1.00782503207
H2O_181 1.00782503207 + 17.9991610 + 1.00782503207
H2O2 34.01468
IO 142.903873
NH3 17.03056
NO 30.00610
NOCl 65.4591
NO2 46.00550
NO3 62.0049
N2 28.01340
N2O 44.0129
N2O5 108.0104
OClO 67.4518
OH 17.00734
O2 32.000
O3 47.99820
O3_666 15.99491461956 + 15.99491461956 + 15.99491461956
O3_667 15.99491461956 + 15.99491461956 + 16.99913170
O3_668 15.99491461956 + 15.99491461956 + 17.9991610
O3_686 15.99491461956 + 17.9991610 + 15.99491461956
O4 63.9976
SF6 146.0554
SO2 64.0638
======= =================================================
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